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On the stability of queueing networks and fluid Dieter Armbruster

Summary: On the stability of queueing networks and fluid
Dieter Armbruster
Erjen Lefeber
and J.E. Rooda
January 11, 2010
The stability of the Lu-Kumar queueing network is re-analyzed. It
is shown that the associated fluid network is a hybrid dynamical system
that has a succession of invariant subspaces leading to global stability. It
is explained why large enough stochastic perturbations of the production
rates lead to an unstable queuing network while smaller perturbations do
not change the stability. The two reasons for the instability are the break-
ing of the invariance of the subspaces and a positive Lyapunov exponent.
A service rule that stabilizes the system is proposed.
1 Introduction
Queueing networks are dynamical networks of production stations and queues,
where customers or lots arrive into a system at random time intervals and get


Source: Armbruster, Dieter - Department of Mathematics and Statistics, Arizona State University


Collections: Mathematics